If teacher pay made a big difference in outcomes, expensive private schools would have very well paid teachers. But private schools typically have lower teacher pay than public schools.
Teacher pay doesn't have as large an influence on student success as it does on how many people are willing to enter the occupation and stay there. Private school teachers typically deal with far fewer students in the classroom and in much better conditions. They also don't typically have to spend as much of their own money on basic school supplies. Improving conditions at public schools and lowering classroom sizes would help to attract teachers too.
Teacher pay doesn't have as large an influence on student success as it does on how many people are willing to enter the occupation and stay there. Private school teachers typically deal with far fewer students in the classroom and in much better conditions. They also don't typically have to spend as much of their own money on basic school supplies. Improving conditions at public schools and lowering classroom sizes would help to attract teachers too.